Find the stationary points of the function z = 3x(x+y)3 - x3 + 24x
z = 3x(x+y)3 - x3 + 24xDifferentiating partially with respect to x and with respect to y:∂z/∂x = 3(x+y)3 + 9x(x+y)2 - 3x2 + 24∂z/∂y = 9x(x+y)2At stationary points: ∂z/∂x = 0 and ∂z/∂y = 0.From ∂z/∂y = 0 we deduce: x = 0 or y = -x.We consider ∂z/∂x = 0 in each of these cases:For x = 0:3y3 + 24 = 0y = -2Hence a stationary point at (0, -2, 0)For y = -x:-3x2 + 24 = 0x = 2√2 and x = -2√2Hence stationary points at (2√2, -2√2, 32√2) and (-2√2, 2√2, -32√2)
HT
Answered by Harvey T. • Further Mathematics tutor
2788 Views
See similar Further Mathematics A Level tutorsRelated Further Mathematics A Level answers
All answers ▸Prove that 27(23^n)+17(10^2n)+22n is divisible by 11 for n belongs to the natural numbers
Unfortunately this box is to small to contain the question so please see the first paragraph of the answer box for the question.
The quadratic equation x^2-6x+14=0 has roots alpha and beta. a) Write down the value of alpha+beta and the value of alpha*beta. b) Find a quadratic equation, with integer coefficients which has roots alpha/beta and beta/alpha.
Understanding differentiation from first principle.